Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
Non-calculatorGCSE Foundation
GCSE Foundation sample Paper 1 (non-calculator)
MathsUKwww.geekhero.co.uk
- 1.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.
- 2.Which of these numbers is a cube number?
- 3.Two mathematically similar cubes have edge lengths 2 cm and 6 cm. Write the ratio of the volume of the smaller cube to the volume of the larger cube in its simplest form.
- 4.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?
- 5.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.
- 6.A bar chart is drawn for a set of categorical data. Write down what the height of each bar represents.
- 7.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.
- 8.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?
- 9.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
- 10.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
- 11.A bag contains 45 sweets. 18 of the sweets are lemon flavour and the rest are orange. A sweet is taken at random, its flavour is recorded, and it is put back in the bag. This is repeated 200 times. Work out how many times you would expect an orange sweet to be taken.
- 12.Oliver uses his calculator to work out 25% of 80 and writes down 320. Without using a calculator, work out the correct value of 25% of 80.
- 13.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
- 14.A fruit bowl contains 9 apples and 21 oranges. Write down the ratio of apples to oranges in its simplest form.
- 15.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.
- 16.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.
- 17.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?
- 18.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
- 19.Work out (3 × 5)²
- 20.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.
How the 20 questions are shared out
- Number — 5 questions (25% of the qualification)
- Algebra — 4 questions (20% of the qualification)
- Ratio, proportion and rates of change — 5 questions (25% of the qualification)
- Geometry and measures — 3 questions (15% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.